A conventional lead frame may include a die attachment pad for accommodating a semiconductor die, as well as a number of leads connected to the semiconductor die. Such a conventional lead frame and semiconductor die may be packaged by being encapsulated within a plastic or resinous material. Various shapes and sizes of such packages exist. For example, U.S. Pat. No. 6,229,200 to Mclellan, entitled “Saw-Singulated Leadless Plastic Chip Carrier,” discloses a chip carrier having an encapsulation encapsulating a semiconductor die. In certain standard and conventional lead frames, the leads connected to the semiconductor die may be spaced somewhat far from the semiconductor die's bonding pads when the die is of a relatively small size compared to the lead frame. Therefore, in connection with certain packages, it may be advantageous to have a lead frame which includes a portion of a lead for attachment to the semiconductor die, and another portion of the lead for connection to an external device.